# The price of aluminum culvert is jointly proportional to its radius and length. If a 12-foot culvert with 6-inch radius costs 324 dollars, then what is the price of a 10-foot culvert with 8-inch radius?

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by hanna0123

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by hanna0123

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thus P = k r l / first find the constant k

324 = k 1/2 * 12

k = 324/6 = 54

then substitute it into the new equation

P = 54 *2/3*10 = 360 dollars

Constant - k (Unit price per ft²)

P - price

r - radius

L - length

Variation equation:

P = k r L

Find the constant:

(Convert inch to ft. ⇒ 6 inch = 0.5 ft)

$324 = k (0.5 ft) (12 ft)

$324 = k (6 ft²)

k = $324/6 ft²

k = $ 54/ft²

If length is 10 ft and radius is 8 inch:

(Convert 8 inch to ft = 2/3 ft)

Price = k r L

Price = ($ 54/ft²) (2/3 ft) (10 ft)

Price = ($54 / ft²) (20/3 ft²)

Price = $ 360